Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.32)

32. 

How many 3-digit numbers are completely divisible 6 ?

[A]. 149
[B]. 150
[C]. 151
[D]. 166

Answer: Option B

Explanation:

3-digit number divisible by 6 are: 102, 108, 114,... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then tn = 996.

a + (n - 1)d = 996

102 + (n - 1) x 6 = 996

6 x (n - 1) = 894

(n - 1) = 149

n = 150

Number of terms = 150.


Ashok Kumar said: (Jan 27, 2011)  
n=[(l-a)/d]+1

n=150

Vivek said: (Apr 29, 2011)  
Adding the given three deghit it means =150
1+5+0/6=remander is 0

Hence if the adding number is not same in divedent and remander is not 0.

Mahesh Patil said: (Aug 1, 2011)  
Total Three digit numbers = 999-100+1 = 900

so numbers Divisible by 6 = 900 / 6 = 150 (Only Quotient ... don't consider the remainder)

Rajkin said: (Nov 12, 2011)  
Thanks mahesh patel.

Sworna said: (Feb 25, 2012)  
@Mahesh.

Why it is 999-100+1? I can't understand please help me.

Neha Nagar said: (Mar 12, 2012)  
@sworna

Dear sworna here +1 is because 100 is also included in three digit no we can not leave 100 here. So it will b better to solve like this....3 digit nos-2 digit nos. So that 999-99=900. Hope you have got it.

Gis said: (Jun 20, 2012)  
@sworna
999-100+1 is taken based on arithmetic progression . last 3-digit no: is 999 and first 3-digit no: is 100 . according to the equation n=(l-a)/d +1
here l=999,a=100, d=1
so n=(999-100)/1 +1=900
hope u can understand

Lalit said: (Jun 23, 2012)  
Another short technique is last 3 digit no is 999 so we divide 999/6= 166 we don't consider decimal part. Now, we only need 3 digit number so 100/6= 16 therefore, 166-16=150 answer.

166 is the total number divisible by 6. We subtracted 100 because before 100 there is only 2 digit number divide by 6.

Ashish said: (Feb 5, 2013)  
If we want to find how many numbers present in 3 digit no which is divisible by any number. Then here is method.

Eg: How many 3-digit numbers are completely divisible 8 ?

Answer:

1000/8=125.

100/8=12 with remainder 4.

125-12=113.

So 113 numbers are divisible from 100 to 999 by 8.

Harpreet said: (May 10, 2013)  
@Ashish total numbers divisible by 8 comes 112 & not 113.

Udaya Santhi said: (Aug 20, 2013)  
6 written as 2*3.

The number completely divisible by both numbers 2&3.

If the number is divisible by 2 that number should be an even.

If the number is divisible by 3 then taken sum of digits.

Option verification:

Only two even numbers are there 150 & 166.

These two numbers are divisible by 2.

1+5+0 = 6(which is divisible by 3), 1+6+6 = 13(which is not divisible by 3).

Hence 150 is the answer.

Swathi said: (Feb 28, 2014)  
149:1+4+9 = 16 it is not divisible by 6.

150:1+5+0 = 6 it is divisible by 6.

151:1+5+1 = 7 not divisible by 6.

166:1+6+6 = 13 not divisible by 6.

Ans :150 (B).

Ishan said: (Aug 1, 2014)  
Directly, on dividing 150 by 6 gives o as a reminder and as a quotient it gives 25 so that 150 comes in the multiple of 25 in the 6 place.

150/6 = 25.

25*6 = 150.

Samir said: (Aug 19, 2014)  
It can take any no.of digit so,

Last digit - first digit(996-102) = 894.

Divide by divisible no. 894/6 = 149.

In formula opposite (n-1) +1.
(149+1) = 150.

Ayushi said: (Jun 27, 2015)  
Divisibility rule of 6.

A no. is divisible by 6 if the no. is even and sum of digit is divisible by 3.

Joshua said: (Jul 13, 2015)  
What if you try the formula for geometric sequence which is an = a1 x r^n-1.

Vicky Kumar Verma said: (Jan 20, 2016)  
999/6 = 166 ignore remainder.

99/6 = 16 ignore remainder.

Now, 166-16 = 150 answer.

Rahul said: (Jul 29, 2016)  
Please give me a solution for "What is the sum of 3 digits number which is completely divisible by 3, then find the sum".

Samir Das said: (Aug 23, 2016)  
Thanks for the answer. It's useful to me.

Rohit said: (Dec 19, 2016)  
100 - 999 these are three digits no,
(last term - first term) + 1 = 900.

And divide 900 by 6 i. e. we obtained 150 is final answer.

Shradha Khirid said: (Jun 28, 2017)  
If no is divisible by 3 and 2 then it is easily divisible by 6.

Tanu said: (Aug 28, 2017)  
Greatest 3 digit number that is divisible by 6 is 996 (q=166).

The smallest is 102(q=17).
Apply simple number rule to count number of values between 166 to 17,
i.e. 166-17+1=150.

Thus this gives you the number of 3 digits divisible by 6.

Damini said: (Sep 16, 2017)  
Write numbers from sequence 149 to 387 like 149150159.

How many time does 1 occur?

Vatsal said: (Dec 5, 2017)  
Number is divided by 6 only when it is perfectly divided by 2 and 3 both.

So Only 150 is divided by both 2 and 3.

Nithya said: (May 25, 2018)  
Divisiablity shortcut for 6 = the number should divide be both 2 & 3.
a. 149 / 2 = no because unit digit is odd.

b. 150 /2 = yes because unit digit ends in 0, then check for 3 -> 150 / 3 = 1+5+0 = 6 = 6/3 = 2, so answer is B.

Tushar said: (Jul 9, 2018)  
Step 1) Consider highest 3 digit number divisible by 3 which is 996, dividing it by 6 we get remainder as 166. Since we want only 3 digit numbers which are divisible by 3 we need to subtract the 2 digit numbers in here.

Step 2) Consider highest 2 digit number divisible by 3 which is 96,dividing it by 6 we get remainder as 16.That means there are 16 (2 digit numbers) divisible by 6.

Step 3) Now subtract these two corresponding remainders we get 166-16 = 150.

Tirtha said: (Nov 12, 2018)  
By taking the multiples of 2*3 for 6 we can operate the divisibility rule for this question.

As for 2, the ending digit should be 0, 2, 4, 6, 8 and for 3 sum of all the digit should be divisible by 3.

So, 150 is divisible by both 2 & 3. This is the correct answer.

Mahesh said: (Aug 20, 2019)  
6 = 2 * 3 which are co-actors, then the number divisible by these two will also divisible by 6.

Amar said: (Sep 2, 2020)  
Lowest 3 digit number which is divisible by 3 is 102.
Highest 3 digit number which is divisible by 3 is 999.
So as per the formula a+(n-1)d=l.
The answer will be 300.

Sahul Hameed said: (Apr 21, 2021)  
As per the Divisibility rule; If last digit is even it will divided by 2 and 3 also divided by 6. In this problem only 166 can sacrifice this method. So the answer is 166.

Anand said: (Jun 27, 2021)  
Let the highest 3 digit num divided by 6 is 996,
then 996/6= 166.

Let the highest 2 digit num divided by 6 is 96,
then 96/6= 16,
Now 166-16= 150.

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